MinT - Best Known (227−53, 227, s)-Nets in Base 4

Best Known (227−53, 227, s)-Nets in Base 4

(227−53, 227, 1040)-Net over F₄ — Constructive and digital

Digital (174, 227, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (174, 228, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 57, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(227−53, 227, 2890)-Net over F₄ — Digital

Digital (174, 227, 2890)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−53, 227, 601793)-Net in Base 4 — Upper bound on s

There is no (174, 227, 601794)-net in base 4, because

1 times m-reduction [i] would yield (174, 226, 601794)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11629 871862 299202 317808 992463 350713 050322 965124 183447 547542 692290 594926 719338 483218 252132 477909 635334 353350 844834 136998 582913 244079 620896 > 4²²⁶ [i]